Fuel cell flow field design for thermal management

ABSTRACT

Fuel cell assemblies comprising at least one thermally compensated coolant channel are provided. The thermally compensated coolant channel has a cross-sectional area that decreases in the coolant flow direction along at least a portion of the channel length. In some embodiments, such thermally compensated coolant channels can be used to provide substantially uniform heat flux, and substantially isothermal conditions, in fuel cells operating with substantially uniform current density.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of and claims priority benefits fromInternational application No. PCT/CA2017/050358 filed on Mar. 21, 2017entitled, “Fuel Cell Flow Field Design For Thermal Management” which, inturn, claims priority benefits from U.S. provisional application No.62/311,901 filed on Mar. 22, 2016 also entitled, “Fuel Cell Flow FieldDesign For Thermal Management”. The '358 and '901 applications arehereby incorporated by reference herein in their entireties.

FIELD OF THE INVENTION

The present invention relates generally to electrochemical fuel cellsand, more specifically, to an electrochemical fuel cell wherein thedesign of the coolant flow field plate provides improved thermalmanagement.

BACKGROUND OF THE INVENTION

Temperature control, and devices designed to provide heating andcooling, are at the heart of many consumer and industrial products. Suchproducts include micro-processors, automobiles, fuel cells, furnaces,hot water heaters, cellular devices, and industrial equipment. Thesedevices make use of some type of heat exchanger to transfer heat fromone place to another.

A heat exchanger is a device that transfers heat from one medium toanother through a heat transfer surface. The heat transfer distributionacross the heat transfer surface is dependent on the temperaturedifference between surface and fluid, exchanger surface area, exchangermass flow, exchanger flow configuration, material properties, and heattransfer mode, among other things.

One common mode of thermal management is through forced convective heattransfer. Here, a working fluid, which is either hotter or colder thanthe heat transfer surface (depending on whether the application is forheating or cooling) is pumped over the heat transfer surface. As itflows over the heat transfer surface, the working fluid temperaturechanges, thereby reducing the temperature difference between the workingfluid and the heat transfer surface. If the heat transfer surface ismaintained at a constant temperature, then heat is transferred to theworking fluid non-uniformly over the heat transfer surface.

It is desirable for some applications for a heat transfer surface to bemaintained at a constant temperature and the heat transfer to besubstantially uniform. One approach to achieving this is to use aworking fluid with a high thermal mass. Working fluids with higherdensity and higher heat capacity typically have higher thermal masses.For example, water has a higher thermal mass than air. Using a workingfluid with a high thermal mass can reduce the variation over the heattransfer surface of the temperature difference between the working fluidand the heat transfer surface, but does not eliminate it entirely.Furthermore, fluids with higher density or higher thermal mass can beassociated with higher parasitic loads; for example, for pumping orotherwise moving the fluid across the heat transfer surface.

Another approach to maintaining a heat transfer surface at a constanttemperature is to use a working fluid that undergoes a phase change (forexample, by heating a liquid to cause it to evaporate). A disadvantageof using a working fluid that undergoes a phase change is that theoperating conditions of the heat exchanger can be restricted totemperature ranges dependent on the physical properties of the workingfluid and can be limited by the phase energy capacity of the workingfluid.

Solid polymer fuel cells are electrochemical devices that produceelectrical power and water from a fuel, such as hydrogen, and oxygen. Asingle solid polymer fuel cell comprises an ion exchange membraneseparating an anode and a cathode. The anode-membrane-cathode assembly,or “membrane electrode assembly”, is interposed between a pair ofelectrically conductive reactant flow field plates that collect current,facilitate the access of the fuel and oxidant to the anode and cathodesurfaces, respectively, and provide for the removal of water formedduring the operation of the fuel cell. A plurality of fuel cellassemblies are usually arranged to form a fuel cell stack.

The fuel cell reaction is exothermic, and the operating temperature ofconventional solid polymer fuel cells is often regulated by a coolantfluid circulation system. To maintain an appropriate cell temperature,coolant channels are generally interposed between the reactant flowfield plates of adjacent fuel cell pairs in a fuel cell stack. Thechannels can be formed in the reactant flow field plates or in separatecoolant plates. A coolant fluid (commonly water or air) is directedthrough the coolant channels to absorb heat energy released by theexothermic electrochemical reaction within the fuel cells. The heat istransferred to the coolant as a result of the thermal gradient betweenthe reaction site and the coolant.

In conventional fuel cells, power is not produced evenly across the fuelcell active area. In other words, the fuel cell does not generallyoperate with uniform current density. Fuel cell cooling systems aregenerally designed to try to reduce the non-uniformity of temperaturedistribution that occurs across an operating fuel cell. Thus,conventional fuel cell cooling systems are deliberately non-uniform,with the heat flux varying across the heat transfer area, to compensatefor non-uniform production of heat. In other words, the cooling systemis configured so that there is a greater capacity for cooling in theregion of the fuel cell where the most heat is being generated.

More recently, fuel cells have been developed that are capable ofoperating with substantially uniform current density. Thermal managementof such fuel cells can be challenging. Use of conventional fuel cellcooling systems will tend to result in an undesirable thermal gradientacross the active area of the fuel cell because heat flux with suchconventional cooling systems is not uniform. This can cause problems,including with product water management, particularly at high currentdensities.

SUMMARY OF THE INVENTION

A fuel cell assembly comprises a plurality of stacked fuel cells, andeach fuel cell comprises an anode, a cathode, a proton exchange membraneelectrolyte interposed between the anode and the cathode, an anode flowfield plate adjacent the anode, the anode flow field plate comprising ananode flow channel for directing fuel to the anode, and a cathode flowfield plate adjacent the cathode, the cathode flow field platecomprising a cathode flow channel for directing oxidant to the cathode.The fuel cell assembly further comprises a thermally compensated coolantchannel interposed between the cathode flow field plate of one of thefuel cells and the anode flow field plate of an adjacent fuel cell, fordirecting a coolant in contact with (or in a heat transfer relationshipwith) at least one of the flow field plates. The thermally compensatedcoolant channel has a cross-sectional area that decreases in the coolantflow direction along at least a portion of the length of the thermallycompensated coolant channel. In some embodiments, the fuel cell assemblycomprises a plurality of anode flow channels and/or a plurality ofcathode flow channels. In some embodiments, the fuel cell assemblycomprises a plurality of thermally compensated coolant channelsinterposed between the cathode flow field plate of one of the fuel cellsand the anode flow field plate of an adjacent fuel cell, for directing acoolant in contact with (or in a heat transfer relationship with) atleast one of the flow field plates.

In some embodiments, the cross-sectional area of the thermallycompensated coolant channel decreases in a non-linear fashion in thecoolant flow direction along at least a portion of the length of thethermally compensated coolant channel.

In some embodiments, the thermally compensated coolant channel has asubstantially rectangular cross-section and the width of the thermallycompensated coolant channel decreases in a non-linear fashion in thecoolant flow direction along at least a portion of the length of thethermally compensated coolant channel.

In some embodiments, the cross-sectional area of the cathode flowchannel and/or the anode flow channel decreases in the reactant flowdirection along at least a portion of the length of the respectivechannel. In some such embodiments, the cathode and/or anode flow channelhas a substantially rectangular cross-section, and the width of thecathode and/or anode channel decreases in accordance with an exponentialfunction along at least a portion of the length of the respectivechannel.

In some embodiments of the fuel cell assemblies and methods foroperating fuel cell assemblies described herein, the thermallycompensated coolant channel can be formed in a coolant flow field platewhich is interposed between the cathode flow field plate of one of thefuel cells in the fuel cell assembly and the anode flow field plate ofan adjacent fuel cell in the fuel cell assembly. In other embodiments ofthe fuel cell assemblies and methods for operating fuel cell assembliesdescribed herein, the thermally compensated coolant channel can beformed in the cathode or anode flow field plate on the opposite surfacefrom the at least one reactant flow channel, or can be formed partiallyin each of the cathode and anode flow field plates so that the thermallycompensated coolant channel is formed by the cooperating surfaces ofadjacent cathode and anode flow field plates.

In some embodiments of the fuel cell assemblies and methods foroperating fuel cell assemblies described herein, the cathode flow fieldplates are stamped to form a plurality of the cathode flow channels onone side thereof, and/or the anode flow field plates are stamped to forma plurality of the anode flow channels on one side thereof. A pluralityof thermally compensated coolant channels can be formed between adjacentpairs of fuel cells in the assembly by the cooperating surfaces of suchanode and cathode flow field plates. In some implementations, thecooperating surfaces of the anode and cathode flow field plates arenested.

A method of operating a fuel cell assembly comprising a plurality offuel cells is provided. Each fuel cell can comprise an anode, a cathode,a proton exchange membrane electrolyte interposed between the anode andthe cathode, an anode flow field plate adjacent the anode, the anodeflow field plate comprising an anode flow channel for directing fuel tothe anode, and a cathode flow field plate adjacent the cathode, thecathode flow field plate comprising a cathode flow channel for directingoxidant to the cathode. The method of operating the fuel cell assemblycomprises:

-   -   supplying fuel and oxidant to the plurality of fuel cells to        generate electrical power from the fuel cells; and    -   directing coolant through a thermally compensated coolant        channel interposed between the cathode flow field plate of one        of the fuel cells and the anode flow field plate of an adjacent        fuel cell, wherein the velocity of the coolant flowing through        the thermally compensated coolant channel increases along at        least a portion the length of the thermally compensated coolant        channel to at least partially compensate for an increase in the        temperature of the coolant along that portion of the length of        the thermally compensated coolant channel. In some embodiments,        the velocity of the coolant flowing through the thermally        compensated coolant channel increases along at least a portion        the length of the thermally compensated coolant channel to        substantially compensate for an increase in the temperature of        the coolant along that portion of the length of the thermally        compensated coolant channel.

In some embodiments of the method, the fuel cells are operated togenerate electrical power with substantially uniform current densityacross each of the fuel cells. The at least one thermally compensatedcoolant channel can be configured to provide substantially uniform heatflux to the coolant flowing through at least a portion of the length ofthe thermally compensated coolant channel, and in some embodiments alongthe entire length of the thermally compensated coolant channel. In someembodiments, the fuel cells are operated substantially isothermally.

In some embodiments, the cross-sectional area of the thermallycompensated coolant channel varies along at least a portion of itslength. For example, the cross-sectional area of the thermallycompensated coolant channel can decrease in a non-linear fashion in thecoolant flow direction along at least a portion of the length of thethermally compensated coolant channel. In some embodiments, thethermally compensated coolant channel has a substantially rectangularcross-section, and the width of the channel decreases in a non-linearfashion in the coolant flow direction along at least a portion of thelength of the thermally compensated coolant channel. In some embodimentsof the method, the cross-sectional area of the cathode flow channeland/or the anode flow channel decreases in the reactant flow directionalong at least a portion of the length of the respective channel. Insome such embodiments, the cathode and/or anode flow channel has asubstantially rectangular cross-section, and the width of the channeldecreases in accordance with an exponential function along at least aportion of the length of the respective channel.

In some embodiments of the fuel cell assemblies and methods of operatingfuel cell assemblies described above, characteristics of the thermallycompensated coolant channel vary continuously or smoothly as a functionof distance along the channel. In other embodiments, characteristics ofthe thermally compensated coolant channel vary as a function of distancealong the channel in a stepwise, discrete or discontinuous manner, forexample, to approximately compensate for the increase in the temperatureof the working fluid along the length of the channel.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an embodiment of a fuel cell coolant flow fieldplate comprising a plurality of thermally compensated channels.

FIG. 2 is a schematic of another embodiment of a fuel cell coolant flowfield plate comprising a plurality of thermally compensated channels.

FIG. 3 is a schematic of a thermally compensated channel.

FIGS. 4 and 5 are flowcharts illustrating a method for configuring athermally compensated channel.

FIG. 6 is a graph illustrating channel width and working fluid velocityalong a thermally compensated rectangular channel configured accordingto the method of FIGS. 4 and 5.

FIG. 7 is a graph illustrating the heat flux and temperature of theworking fluid along a thermally compensated rectangular channelconfigured according to the method of FIGS. 4 and 5.

FIG. 8 is a graph illustrating the temperature of the working fluidalong the length of a channel for conventional and thermally compensatedchannels.

FIG. 9 is a graph that shows that the heat flux is essentially constantalong the length of the thermally compensated channel from the inlet tothe outlet.

FIG. 10 is a graph of channel width as a function of normalized distancealong the channel from inlet to outlet for conventional and thermallycompensated channels.

FIG. 11 is a graph of the velocity of working fluid as a function ofnormalized distance along the channel from inlet to outlet forconventional and thermally compensated channels.

FIG. 12 is a schematic of an apparatus used to verify the method ofFIGS. 4 and 5 for configuring a thermally compensated channel.

FIG. 13 is a graph of the test results and the expected temperatureprofile, based on the thermal model, for conventional serpentinechannels.

FIG. 14 is a graph of the test results and the expected temperatureprofile, based on the thermal model, for thermally compensated channels.

FIGS. 15A-C illustrate an example embodiment of a pair of corrugated,trapezoidal reactant flow field plates that are stacked so that coolantchannels having a cross-sectional area that varies along their lengthare formed between the cooperating corrugated surfaces of the stackedplates.

FIGS. 16A-C illustrate an example embodiment of a pair of corrugated,trapezoidal reactant flow field plates that are nested so that coolantchannels having a cross-sectional area that varies along their lengthare formed between the cooperating corrugated surfaces of the nestedplates.

FIGS. 17A-C illustrate another example embodiment of a pair ofcorrugated, trapezoidal reactant flow field plates that are nested sothat coolant channels having a cross-sectional area that varies alongtheir length are formed between the cooperating corrugated surfaces ofthe nested plates.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT(S)

In embodiments of the technology described herein, the velocity of theworking fluid over the heat transfer surface is adjusted to control thevariation of heat flux (heat transfer per unit area) over the heattransfer surface. The velocity of the working fluid can be adjusted toreduce or eliminate the variation in heat flux over the heat transfersurface. If the heat flux is substantially uniform and heat is producedsubstantially uniformly by the heat source, then the resultingtemperature of the heat transfer surface will also be substantiallyuniform.

An advantage of achieving uniform temperature of the heat transfersurface and substantially uniform heat flux is that it can increase theheat transfer capacity of the heat exchanger. As a consequence, aworking fluid with a lower thermal mass can be used to remove the sameamount of heat, thereby reducing the parasitic power losses associatedwith pumping coolant at a higher flow rate to accommodate a fluid ordesign with poorer heat transfer characteristics. Another advantage ofcertain embodiments of the technology described herein is that a phasechange is not required to achieve substantially uniform heat flux, andso a wide variety of working fluids and broad range of operatingtemperatures can be used.

FIG. 1 is a schematic of an embodiment of fuel cell coolant flow fieldplate 100 comprising a plurality of thermally compensated channels 110.Coolant flow field plate 100 further comprises inlet 140 and outlet 150.Thermally compensated channels 110 are configured such that the width ofchannels nearer inlet 140, for example, in region 120, is greater thanthe width of channels nearer outlet 150, for example, in region 130.

FIG. 2 is a schematic of another embodiment of fuel cell coolant flowfield plate 200 comprising a plurality of thermally compensated channels210. Coolant flow field plate 200 further comprises inlet 240 and outlet250. Thermally compensated channels 210 are configured such that thewidth of channels nearer inlet 240, for example, in region 220 isgreater than the width of channels nearer outlet 250, for example, inregion 230.

In some embodiments, thermally compensated channels (such as 110 of FIG.1 or 210 of FIG. 2) can have a rectangular cross-section, or they canhave a substantially rectangular cross-section, for example with roundedcorners and slightly flared side-walls. In other embodiments, thermallycompensated channels can have other cross-sectional shapes including,but not limited to, trapezoidal, triangular, semi-circularcross-sections.

FIG. 3 is schematic of thermally compensated channel 300, such as anindividual channel on a coolant flow field plate. Thermally compensatedchannel 300 has a rectangular cross-section, and comprises heat transfersurface 310. Heat flow across heat transfer surface 310 from a fuel cell(not shown in FIG. 3) is illustrated by arrows 320. The flow of aworking fluid entering thermally compensated channel 300 at inlet 330 isillustrated by arrow 335. The flow of a working fluid leaving thermallycompensated channel 300 at outlet 340 is illustrated by arrow 345.

FIGS. 4 and 5 are flowcharts illustrating method 400 for configuring athermally compensated channel. Method 400 comprises a numerical approachthat estimates heat flux at a plurality of equally spaced positionsalong the length of the channel from the inlet to the outlet.

FIG. 4 is a flowchart illustrating a first part of method 400. The firstpart of method 400 comprises steps 410 through 480.

At step 410, the channel is configured with an initial set ofparameters, the initial set of parameters comprising depth D₀ and widthW₀ at the inlet, length of the channel L, mass flow of the working fluid{dot over (m)}, temperature of the working fluid at the inlet T₀, andthe wall temperature T_(w).

At step 420, the incremental distance Δx between each of the pluralityof equally spaced positions is selected. The incremental distance isselected to provide a desired level of accuracy for the resulting widthprofile of the channel.

At step 430, method 400 estimates the velocity of the working fluid atthe inlet, referred to as the initial velocity v₀ of the working fluid,using equation (1), where {dot over (m)} is the mass flow rate, and ρ₀is the density of the working fluid at the inlet:

$\begin{matrix}{v_{0} = \frac{\overset{.}{m}}{\rho_{0}W_{0}D_{0}}} & (1)\end{matrix}$

At step 440, method 400 estimates the hydraulic diameter d_(h0) of thechannel at the inlet, using equation (2):

$\begin{matrix}{d_{h\; 0} = \frac{4W_{0}D_{0}}{2\left( {W_{0} + D_{0}} \right)}} & (2)\end{matrix}$

At step 450, method 400 estimates the physical properties of the workingfluid at the inlet temperature T₀. The physical properties comprisedensity ρ, dynamic viscosity μ, specific heat C_(p), and thermalconductivity k_(th).

At step 460, method 400 estimates the convective heat transfercoefficient h₀ at the inlet temperature using equations (3) through (6)as follows:

$\begin{matrix}{h_{0} = \frac{k_{{th}\; 0}{Nu}_{0}}{d_{h\; 0}}} & (3) \\{{Nu}_{0} = {1.86\left( {\Pr\mspace{11mu}{Re}\frac{d_{h\; 0}}{L}} \right)^{\frac{1}{3}}\left( \frac{\mu_{0}}{\mu_{w}} \right)^{0.14}}} & (4) \\{\Pr_{0} = \frac{C_{p\; 0}\mu_{0}}{k_{{th}\; 0}}} & (5) \\{{Re}_{0} = \frac{\rho_{0}v_{0}d_{h\; 0}}{\mu_{0}}} & (6)\end{matrix}$

where Nu is the Nusselt number, Re is the Reynolds number, and Pr is thePrandtl number.

At step 470, method 400 estimates the local heat flux, q, using equation(7):q(0)=h ₀(T _(w) −T ₀)  (7)

At step 480, method estimates the heat transfer, Q, across the initialheat transfer area using equation (8):Q=q(0)W ₀ Δx  (8)

Method 400 proceeds to step 510 of FIG. 5.

FIG. 5 is a flowchart illustrating a second part of method 400. Thesecond part of method 400 comprises steps 510 through 550.

At step 510, method 400 increments the current position along thechannel by adding the incremental distance Δx to the previous position.

At step 520, if the current position along the channel exceeds channellength L, then method 400 proceeds to step 530. At step 530, widthprofile W(x) is output to a storage or display device suitable forserving as input to the configuration of a thermally compensated channelin a fuel cell flow plate. Method 400 proceeds to step 540 and ends.

At step 520, if the current position along the channel does not exceedchannel length L, then method 400 proceeds to step 550. At step 550,method 400 estimates the temperature T_(i) of the working fluid at thecurrent position x_(i) along the channel using equation (9):

$\begin{matrix}{T_{i} = {\frac{Q_{i - 1}}{\overset{.}{m}\; C_{{pi} - 1}} + T_{i - 1}}} & (9)\end{matrix}$where Q_(i-1) is the heat transfer across the heat transfer area at theprevious position x_(i-1) along the channel, {dot over (m)} is the massflow rate, C_(pi-1) is the specific heat at position x_(i-1) and T_(i-1)is the temperature of the working fluid at position x_(i-1).

At step 560, method 400 solves for substantially constant heat flux byadjusting channel width W(x). In other words, method 400 finds channelwidth W(x) for which the absolute difference in heat flux betweenq(x_(i)) and q(x_(i-1)) is below a predetermined threshold.Alternatively, method 400 can be used to tailor a specific heat fluxgradient or profile (for example so that the temperature differenceacross a fuel cell can be controlled). The solver uses equations (10)through (16):

$\begin{matrix}{h_{i} = \frac{k_{thi}{Nu}_{i}}{d_{hi}}} & (10) \\{{Nu}_{i} = {1.86\left( {\Pr\mspace{11mu}{Re}\frac{d_{h\; i}}{L}} \right)^{\frac{1}{3}}\left( \frac{\mu_{i}}{\mu_{w}} \right)^{0.14}}} & (11) \\{\Pr_{i} = \frac{C_{p\; i}\mu_{i}}{k_{{th}\; i}}} & (12) \\{{Re}_{i} = \frac{\rho_{i}v_{i}d_{h\; i}}{\mu_{i}}} & (13) \\{d_{h\; i} = \frac{4W_{i}D_{0}}{2\left( {W_{i} + D_{0}} \right)}} & (14) \\{v_{i} = \frac{\overset{.}{m}}{\rho_{i}W_{i}D_{0}}} & (15) \\{{q\left( x_{i} \right)} = {h_{i}\left( {T_{w} - T_{i}} \right)}} & (16)\end{matrix}$

A suitable numerical solver can be used such as a Generalized ReducedGradient algorithm for solving non-linear problems.

When the numerical solver has converged to a solution for channel widthW(x_(i)), method 400 proceeds to step 570. At step 570, channel widthW(x_(i)) is stored in a channel width profile record.

At step 580, method 400 estimates the heat transfer across the currentheat transfer area W(x_(i))Δx using equation (17):Q _(i) =q(x _(i))W _(i) Δx  (17)

Method 400 then returns to step 510.

Method 400 describes the method for configuring a thermally compensatedchannel for a channel having a rectangular cross-section with a varyingwidth and a substantially constant depth along its length. In otherembodiments, a thermally compensated channel can have a rectangularcross-section with a varying or constant width and a varying depth. Insome embodiments, a thermally compensated channel can have across-section that is not rectangular or substantially rectangular, buthas some other cross-sectional channel shape. A thermally compensatedchannel can be configured by a suitable adjustment of the velocity ofthe working fluid in the channel through the appropriate alteration inthe channel's cross-sectional area.

FIG. 6 is a graph illustrating channel width and working fluid velocityalong a thermally compensated channel with rectangular cross-sectionconfigured according to method 400 of FIGS. 4 and 5.

The channel width decreases from 2.5 mm at the inlet to approximately1.1 mm at the outlet. The decreasing channel width is associated with acorresponding increase in velocity of the working fluid along thechannel length. The velocity increases from approximately 0.185 m/s atthe inlet to 0.418 m/s at the outlet.

FIG. 7 is a graph illustrating the heat flux and temperature of theworking fluid along a thermally compensated rectangular channelconfigured according to method 400 of FIGS. 4 and 5.

The heat flux is held essentially constant. In the example shown, theheat flux is approximately 12.7 W/cm². The temperature of the workingfluid increases along the channel from 25° C. at the inlet toapproximately 41.3° C. at the outlet.

FIG. 8 is a graph illustrating the temperature of the working fluidalong the length of a channel for a conventional channel and for athermally compensated channel. Line 810 shows the variation intemperature of the working fluid along the length of a conventionalchannel. In this example, the conventional channel has a rectangularcross-section and constant width, depth and cross-sectional area alongits length. Line 820 shows the variation in temperature of the workingfluid along the length of a thermally compensated channel such as theone illustrated in FIGS. 6 and 7.

FIG. 8 shows that more heat is removed from the fuel cell by aconfiguration comprising thermally compensated channels since thetemperature of the working fluid at the outlet is higher than it is forthe conventional channel, even though the inlet temperature at eachinlet is the same.

FIG. 9 is a graph illustrating the heat flux along the length of achannel for a conventional channel and a thermally compensated channel.Line 910 shows the heat flux along the length of a conventional channel.In this example, the conventional channel has a rectangularcross-section and constant width, depth and cross-sectional area alongits length. Line 920 shows the heat flux along the length of a thermallycompensated channel such as the one illustrated in FIGS. 6 and 7.

FIG. 9 shows that the heat flux can be essentially constant along thelength of the thermally compensated channel from the inlet to theoutlet. Since the thermally compensated channel is configured to keepthe heat flux essentially constant along the length of the channel, heatis removed more uniformly and isothermal operation is possible.

FIG. 10 is a graph of the channel width as a function of normalizeddistance along the channel from inlet to outlet for a conventionalchannel and a thermally compensated channel. Line 1010 shows the channelwidth of a conventional channel having essentially constant channelwidth. Line 1020 shows the channel width of a thermally compensatedchannel, such as the one illustrated in FIGS. 6 and 7.

FIG. 11 is a graph of the velocity of working fluid as a function ofnormalized distance along the channel from inlet to outlet for aconventional channel and a thermally compensated channel. Line 1110shows the velocity of working fluid along the length of a conventionalchannel having substantially constant channel width, depth andcross-sectional area along its length. Line 1120 shows the velocity ofworking fluid along the length of a thermally compensated channel suchas the one illustrated in FIGS. 6 and 7.

The method described above is one approach to configuring a thermallycompensated channel. Other suitable methods for adjusting the dimensionsof the channel, the velocity of the working fluid and/or the local heattransfer area can be used to configure a channel to substantiallycompensate for the increase in the temperature of the working fluidalong the length of the channel or, in other words, to compensate forthe decrease in the temperature difference between the working fluid andthe heat transfer surface along the length of the channel.

An experiment was conducted in order to validate the method describedabove for configuring a thermally compensated channel. The experimentcompared the behavior of a conventional channel to the behavior of athermally compensated channel.

FIG. 12 is a schematic of apparatus 1200 used to verify the method ofFIGS. 4 and 5 for configuring a thermally compensated channel. Apparatus1200 comprises simulated reactant flow field plate 1210, coolant flowfield plate 1220, clamping plates 1230A and 1230B, inlet and outletports 1240A and 1240B for hot fluid, inlet and outlet ports 1250A and1250B for cold fluid, and one or more thermocouples 1260A through 1260D.

Simulated reactant flow field plate 1210 was maintained at anessentially constant temperature to simulate a fuel cell operating atuniform current density. Coolant flow field plate 1220 comprises anarrangement of channels. In a first embodiment, the channels areconventional channels arranged in a serpentine pattern. In a secondembodiment, the channels are thermally compensated channels andconfigured to produce uniform heat flux across the heat transfer area.Thermocouples 1260A through 1260D were used to measure the temperatureof fluid flowing across coolant flow field plate 1220.

Simulated reactant flow field plate 1210 is situated on the hot side ofthe heat exchanger. Fluid in flow field plate 1210 has a mass flow rateof {dot over (m)}_(h), and the temperature of the fluid at inlet andoutlet ports 1240A and 1240B is T_(hi) and T_(ho) respectively.

Coolant flow field plate 1220 is situated on the cool side of the heatexchanger. Fluid in controlled flow field plate 1220 has a mass flowrate of {dot over (m)}_(c), and the temperature of the fluid at inletand outlet ports 1250A and 1250B is T_(ci) and T_(co) respectively.

Simulated reactant flow field plate 1210 and coolant flow field plate1220 cover an equivalent active area. The working fluid was deionizedwater. To avoid temperature gradients on the hot side of the heatexchanger, the deionized water was pumped across plate 1210 atsignificantly higher flow rates on the hot side relative to the coldside.

A first test was conducted using the first embodiment of coolant flowfield plate 1220 (serpentine channels). Table 1 lists the parameters forthe first test.

TABLE 1 Parameter Serpentine Channels T_(ci) [° C.] 23 T_(co) [° C.] 60T_(hi) [° C.] 68 T_(ho) [° C.] 64 Channel Length [m] 2.1 W₀ [m] 0.0016D₀ [m] 0.00400 {dot over (m)}_(c) [kg/s] 0.00067 {dot over (m)}_(h)[kg/s] 0.033

FIG. 13 is a graph displaying the test results and the expectedtemperature profile for serpentine channels. FIG. 13 shows there is goodagreement between the expected temperature profile 1310 (calculatedusing a model) and data points 1320A through 1320D measured bythermocouples 1260A through 1260D respectively of FIG. 12. The root meansquare error is less than 2° C.

A second test was conducted using the second embodiment of coolant flowfield plate 1220 (thermally compensated channels). Table 2 lists theparameters for the second test.

There are a variety of suitable configurations of the channel geometrythat can be used to compensate at least partially for the increase intemperature of the working fluid along the length of the channel. Forthe purposes of the second test, the channel was configured to have asubstantially rectangular cross-section, a constant depth, and a channelwidth configured to follow an exponential function with respect to theposition along the channel length, and a y-intercept of 0.0025 and abase of 0.00278.

TABLE 2 Parameter Thermally Compensated Channels T_(ci) [° C.] 24 T_(co)[° C.] 45 T_(hi) [° C.] 68 T_(ho) [° C.] 60 Channel Length [m] .1505 W₀[m] 0.0025 D₀ [m] 0.00300 {dot over (m)}_(c) [kg/s] 0.0050 {dot over(m)}_(h) [kg/s] 0.033

FIG. 14 is a graph of the test results and the expected temperatureprofile for thermally compensated channels. FIG. 14 shows there is goodagreement between the expected temperature profile 1410 (calculatedusing a model) and data points 1420A through 1420D measured bythermocouples 1260A through 1260D respectively of FIG. 12. The root meansquare error is less than 2° C.

In some embodiments, a fuel cell flow field plate comprises at least onecooling channel with a cross-sectional area or width that decreases frominlet to outlet. In some embodiments, the cross-sectional area or widthof the cooling channel decreases continuously from inlet to outlet.

In some embodiments, a fuel cell flow field plate comprises at least onechannel for convective cooling, the channel comprising a first region inwhich the channel has a substantially constant cross-sectional area orwidth, and a second region in which the channel has a diminishingcross-sectional area or width. The first region may facilitate thedistribution of a working fluid from an inlet port to the fuel cell flowfield plate. The second region may facilitate the distribution of theworking fluid across the fuel cell flow field plate from the firstregion to an outlet port.

In some embodiments, a fuel cell flow field plate comprises at least onechannel for convective cooling, the channel comprising a first region inwhich the channel has a substantially constant cross-sectional area orwidth, a second region following the first region in which the channelhas a diminishing cross-sectional area or width, and a third regionfollowing the second region in which the channel has a substantiallyconstant cross-sectional area or width.

Embodiments of the apparatus and method described above can be used toconfigure thermally compensated coolant channels for fuel cells havingconventional cathode and anode flow field designs such as cathode andanode flow field designs and operating with non-uniform current density.

Embodiments of the apparatus and method described above can be used toconfigure thermally compensated coolant channels that are particularlysuitable for use in fuel cells operating with substantially uniformcurrent density; for example, having unconventional reactant flow fieldchannels on the anode and/or the cathode.

Fuel cell cathode and anode flow channels having a cross-sectional areathat varies along the channel length in various manners are described inApplicant's U.S. Pat. No. 7,838,169, which is herein incorporated byreference in its entirety, and in Applicant's U.S. Patent ApplicationPublication No. US2015/0180052 which is also herein incorporated byreference in its entirety. Under certain operating conditions, fuelcells with reactant channel profiles as described in these documents canbe operated with substantially uniform current density, and also atextremely high current densities where thermal management can bechallenging. In these situations, it can be particularly desirable toconfigure the fuel cell coolant channels to be able to providesubstantially uniform heat flux across the fuel cell active area when asuitable coolant is directed through them. For example, this approachcan be used for fuel cells in motive applications, operating at highcurrent densities in the range of about 1 A/cm² to about 2 A/cm², orabout 1 A/cm² to about 3 A/cm², and in some cases at operating atcurrent densities exceeding 3 A/cm².

Thus, aspects of the apparatus and methods described herein relate tofuel cell assemblies comprising thermally compensated coolant channelsin combination with oxidant and/or fuel reactant channels having specialprofiles (such as described in U.S. Pat. No. 7,838,169 and U.S. PatentApplication Publication No. US2015/0180052), and methods for operatingsuch fuel cell assemblies, for example, to provide substantially uniformcurrent density and substantially uniform heat flux between the fuelcell and the coolant across the fuel cell active area. This can allow asubstantially uniform plate temperature, or substantially isothermalconditions, to be maintained across the fuel cell active area duringoperation of the fuel cell. This can in turn aid in maintaining on-goinguniformity of current density.

In some embodiments, a fuel cell comprises:

an anode;

a cathode;

a proton exchange membrane electrolyte interposed between the anode andthe cathode;

an anode flow field plate adjacent the anode, the anode flow field platecomprising at least one anode flow channel for directing fuel to theanode;

a cathode flow field plate adjacent the cathode, the cathode flow fieldplate comprising at least one cathode flow channel for directing oxidantto the cathode; and

at least one thermally compensated coolant channel between the cathodeflow field plate and the anode flow field plate, for directing a coolantin contact with at least one of the flow field plates.

The thermally compensated coolant channel has a cross-sectional areathat decreases in the coolant flow direction along at least a portion ofthe channel length. In some embodiments, the channel is substantiallyrectangular in cross-section and the width of the channel decreasesnon-linearly while the depth remains substantially constant.

In some embodiments, the cross-sectional area of the at least onecathode flow channel decreases in the oxidant flow direction along atleast a portion of the channel length and/or the cross-sectional area ofthe at least one anode flow channel decreases in the fuel flow directionalong at least a portion of the channel length. In some embodiments, thecross-sectional area of the at least one cathode flow channel and/or theat least one anode flow channel decreases in accordance with anexponential function. In such embodiments in which the cross-sectionalarea of the anode or cathode flow channels decreases in the reactantflow direction along at least a portion of the length of the respectivechannel, the characteristics of these reactant flow channels can varycontinuously and smoothly as a function of distance along the channel,or can vary in stepwise, discrete or discontinuous manner, such asdescribed in co-owned U.S. Patent Application Publication No.US2015/0180052, for example.

Similarly, in some embodiments of a thermally compensated coolantchannel, characteristics of the coolant channel (such as cross-sectionalarea or width) or the velocity of the working fluid, for example, varycontinuously or smoothly as a function of distance along the channel. Inother embodiments, characteristics of a thermally compensated coolantchannel vary as a function of distance along the channel in a stepwise,discrete or discontinuous manner, for example, to approximatelycompensate for the increase in the temperature of the working fluidalong the length of the channel. For example, performance benefits canbe obtained by using thermally compensated coolant channels thatincorporate discrete variations, such as for example, a step-wisedecrease in cross-sectional area along at least a portion of thechannel, or a cross-sectional area that decreases in accordance with apiecewise linear function along at least a portion of the channellength. In some embodiments, thermally compensated coolant channels cancontain discrete features that reduce the effective cross-sectional areaand obstruct coolant flow, where the density and/or size of thosefeatures increases in the coolant flow direction to decrease thecross-sectional area and/or increase the flow velocity on average in theflow direction along the channel. Examples of such features are ribs,tapered ribs or pillars.

The fuel cell reactant flow field plates and coolant flow field platescan be made from a suitable electrically conductive material, includinggraphite, carbon, composite materials and various metals. Depending onthe plate material, the channels can be formed by milling, molding,stamping, embossing or corrugating, for example. The coolant channelscan be formed in separate coolant flow field plates, or can be formed inthe anode and/or cathode reactant flow field plates on the oppositesurface from the reactant channels.

In some embodiments of the fuel cell assemblies, the reactant flow fieldplates are stamped, embossed or corrugated so that channels are formedon both sides. Such plates can be stacked or nested so that coolantchannels are formed between the cooperating surfaces of the anode andcathode flow field plates. If the anode and cathode flow field channelshave a cross-sectional area that varies along the channel length, thecorresponding channel on the opposite face of each plate will also havea cross-sectional area that varies along the channel length.

For example, FIGS. 15A-C show a pair of corrugated, trapezoidal reactantflow field plates, 151 and 153, that are stacked one on top of theother. FIG. 15A shows a cross-sectional view of anode plate 151 on topof cathode plate 153. FIG. 15B shows an enlarged view of a portion ofFIG. 15A, with fuel flow channels 152 on the upper surface of anodeplate 151, and oxidant flow channels 154 on the lower surface of cathodeplate 153. Coolant channels 155 are formed between the cooperatingcorrugated surfaces of the pair of stacked plates 151 and 153. FIG. 15Cis an isometric view of corrugated, trapezoidal reactant flow fieldplates 151 and 153 stacked to define coolant channels 155 between theircooperating surfaces. The cross-sectional area of the fuel, oxidant andcoolant channels, 152, 154 and 155, respectively, varies along theirlength.

FIGS. 16A-C show a pair of corrugated, trapezoidal reactant flow fieldplates, 161 and 163, that are nested together. FIG. 16A shows across-sectional view of anode plate 161 on top of cathode plate 163.FIG. 16B shows an enlarged view of a portion of FIG. 16A, with fuel flowchannels 162 on the upper surface of anode plate 161, and oxidant flowchannels 164 on the lower surface of cathode plate 163. Coolant channels165 are formed between the cooperating corrugated surfaces of the pairof nested plates 161 and 163. FIG. 16C is an isometric view ofcorrugated, trapezoidal reactant flow field plates 161 and 163 nested todefine coolant channels 165 between their cooperating surfaces. Thecross-sectional area of the fuel, oxidant and coolant channels, 162, 164and 165, respectively, varies along their length.

FIGS. 17A-C show a pair of corrugated, trapezoidal reactant flow fieldplates, 171 and 173, that are also nested together. FIG. 17A shows across-sectional view of anode plate 171 on top of cathode plate 173.FIG. 17B shows an enlarged view of a portion of FIG. 17A, with fuel flowchannels 172 on the upper surface of anode plate 171, and oxidant flowchannels 174 on the lower surface of cathode plate 173. A pair ofcoolant channels, 175A and 175B, is formed by the cooperating corrugatedsurfaces for each channel of the nested plates 171 and 173. FIG. 17C isan isometric view of corrugated, trapezoidal reactant flow field plates171 and 173 nested to define pairs of coolant channels, 175A and 175B,between their cooperating surfaces. The cross-sectional area of thefuel, oxidant and coolant channels, 172, 174, 175A and 175B,respectively, varies along their length.

While particular elements, embodiments and applications of the presentinvention have been shown and described, it will be understood, that theinvention is not limited thereto since modifications can be made bythose skilled in the art without departing from the scope of the presentdisclosure, particularly in light of the foregoing teachings.

What is claimed is:
 1. A fuel cell assembly comprising: (a) a first fuelcell comprising: (i) a first anode; (ii) a first cathode; (iii) a firstproton exchange membrane electrolyte interposed between said first anodeand said first cathode; (iv) a first anode flow field plate adjacent tosaid first anode, said first anode flow field plate comprising a firstanode flow channel for directing a fuel to said first anode; and (v) afirst cathode flow field plate adjacent to said first cathode, saidfirst cathode flow field plate comprising a first cathode flow channelfor directing an oxidant to said first cathode, wherein across-sectional area of said first cathode flow channel decreases in aflow direction of said oxidant along at least a portion of the length ofsaid first cathode flow channel; (b) a second fuel cell comprising: (i)a second anode; (ii) a second cathode; (iii) a second proton exchangemembrane electrolyte interposed between said second anode and saidsecond cathode; (iv) a second anode flow field plate adjacent to saidsecond anode, said second anode flow field plate comprising a secondanode flow channel for directing said fuel to said second anode; and (v)a second cathode flow field plate adjacent to said second cathode, saidsecond cathode flow field plate comprising a second cathode flow channelfor directing said oxidant to said second cathode; and (c) a thermallycompensated coolant channel interposed between said first cathode flowfield plate and said second anode flow field plate, for directing acoolant in a heat transfer relationship with at least one of said firstcathode flow field plate and said second anode flow field plate, saidthermally compensated coolant channel having an inlet, an outlet, and across-sectional area that decreases monotonically in a flow direction ofsaid coolant from said inlet to said outlet of said thermallycompensated coolant channel, such that the width of said thermallycompensated coolant channel near said inlet is greater than the width ofsaid thermally compensated coolant channel near said outlet; whereinsaid first cathode flow field plate comprises a plurality of firstcathode flow channels on a first side of said first cathode flow fieldplate and a corresponding inverse pattern defining a first plurality ofgrooves on a second side of said first cathode flow field plate, andsaid second anode flow field plate comprises a plurality of second anodeflow channels on a first side of said second anode flow field plate anda corresponding inverse pattern defining a second plurality of grooveson a second side of said second anode flow field plate, and wherein aplurality of thermally compensated coolant channels are formed betweensaid first fuel cell and said second fuel cells by the cooperatingsurfaces of said second side of said first cathode flow field plate andsaid second side of said second anode flow field plate.
 2. The fuel cellassembly of claim 1 wherein said cross-sectional area of said thermallycompensated coolant channel decreases continuously in said flowdirection of said coolant along said thermally compensated coolantchannel from said inlet to said outlet.
 3. The fuel cell assembly ofclaim 1 wherein said thermally compensated coolant channel has asubstantially rectangular cross-section, and a width of said thermallycompensated coolant channel decreases in a non-linear fashion in saidflow direction of said coolant along at least a portion of the length ofsaid thermally compensated coolant channel.
 4. The fuel cell assembly ofclaim 1 wherein a cross-sectional area of said second cathode flowchannel decreases in a flow direction of said oxidant along at least aportion of the length of said second cathode flow channel.
 5. The fuelcell assembly of claim 4 wherein said first cathode flow channel andsaid second cathode flow channel each have a substantially rectangularcross-section, and a width of said first cathode flow channel decreasesin accordance with an exponential function along said at least a portionof the length of said first cathode flow channel, and a width of saidsecond cathode flow channel decreases in accordance with an exponentialfunction along said at least a portion of the length of said secondcathode flow channel.
 6. The fuel cell assembly of claim 4 wherein across-sectional area of said first anode flow channel decreases in aflow direction of said fuel along at least a portion of the length ofsaid first anode flow channel, and the cross-sectional area of saidsecond anode flow channel decreases in a flow direction of said fuelalong at least a portion of the length of said second anode flowchannel.
 7. The fuel cell assembly, of claim 6 wherein said first anodeflow channel and said second anode flow channel each have asubstantially rectangular cross-section, and a width of said first anodeflow channel decreases in accordance with an exponential function alongsaid at least a portion of the length of said first anode flow channel,and a width of said second anode flow channel decreases in accordancewith an exponential function along said at least a portion of the lengthof said second anode flow channel.
 8. The fuel cell assembly of claim 1wherein said first cathode flow field plate and said second anode flowfield plate are nested, so that said plurality of first cathodechannels, said plurality of second anode flow channels, and saidplurality of thermally compensated coolant channels are at leastpartially in the same plane.
 9. A fuel cell assembly comprising: (a) afirst fuel cell comprising: (i) a first anode; (ii) a first cathode;(iii) a first proton exchange membrane electrolyte interposed betweensaid first anode and said first cathode; (iv) a first anode flow fieldplate adjacent to said first anode, said first anode flow field platecomprising a first anode flow channel for directing a fuel to said firstanode; and (v) a first cathode flow field plate adjacent to said firstcathode, said first cathode flow field plate comprising a first cathodeflow channel for directing an oxidant to said first cathode, wherein across-sectional area of said first cathode flow channel decreases in aflow direction of said oxidant along at least a portion of the length ofsaid first cathode flow channel; (b) a second fuel cell comprising: (i)a second anode; (ii) a second cathode; (iii) a second proton exchangemembrane electrolyte interposed between said second anode and saidsecond cathode; (iv) a second anode flow field plate adjacent to saidsecond anode, said second anode flow field plate comprising a secondanode flow channel for directing said fuel to said second anode; and (v)a second cathode flow field plate adjacent to said second cathode, saidsecond cathode flow field plate comprising a second cathode flow channelfor directing said oxidant to said second cathode; and (c) a thermallycompensated coolant channel interposed between said first cathode flowfield plate and said second anode flow field plate, for directing acoolant in a heat transfer relationship with at least one of said firstcathode flow field plate and said second anode flow field plate, saidthermally compensated coolant channel having an inlet, an outlet, and across-sectional area that decreases monotonically in a flow direction ofsaid coolant from said inlet to said outlet of said thermallycompensated coolant channel, such that the width of said thermallycompensated coolant channel near said inlet is greater than the width ofsaid thermally compensated coolant channel near said outlet; wherein:said first cathode flow field plate comprises a plurality of firstcathode flow channels on a first side of said first cathode flow fieldplate and a corresponding inverse pattern defining a first plurality ofgrooves on a second side of said first cathode flow field plate, andsaid second anode flow field plate has a first side and a second side,and a plurality of second anode flow channels on said first side of saidsecond anode flow field plate, wherein a plurality of thermallycompensated coolant channels are formed between said first fuel cell andsaid second fuel cells by the cooperating surfaces of said second sideof said first cathode flow field plate and a second side of said secondanode flow field plate; or said first cathode flow field plate comprisesa first side and said second side, and a plurality of first cathode flowchannels on said first side of said first cathode flow field plate, andsaid second anode flow field plate comprises a plurality of said secondanode flow channels on a first side of said second anode flow fieldplate and a corresponding inverse pattern defining a second plurality ofgrooves on a second side of said second anode flow field plate, whereina plurality of thermally compensated coolant channels are formed betweensaid first fuel cell and said second fuel cells by the cooperatingsurfaces of said second side of said first cathode flow field plate andsaid second side of said second anode flow field plate.
 10. The fuelcell assembly of claim 9 wherein said cross-sectional area of saidthermally compensated coolant channel decreases continuously in saidflow direction of said coolant along said thermally compensated coolantchannel from said inlet to said outlet.
 11. The fuel cell assembly ofclaim 9 wherein said thermally compensated coolant channel have asubstantially rectangular cross-section, and a width of said thermallycompensated coolant channel decreases in a non-linear fashion in saidflow direction of said coolant along at least a portion of the length ofsaid thermally compensated coolant channel.
 12. The fuel cell assemblyof claim 9 wherein a cross-sectional area of said second cathode flowchannel decreases in a flow direction of said oxidant along at least aportion of the length of said second cathode flow channel.
 13. The fuelcell assembly of claim 12 wherein said first cathode flow channel andsaid second cathode flow channel each have a substantially rectangularcross-section, and a width of said first cathode flow channel decreasesin accordance with an exponential function along said at least a portionof the length of said first cathode flow channel, and a width of saidsecond cathode flow channel decreases in accordance with an exponentialfunction along said at least a portion of the length of said secondcathode flow channel.
 14. The fuel cell assembly of claim 12 wherein across-sectional area of said first anode flow channel decreases in aflow direction of said fuel along at least a portion of the length ofsaid first anode flow channel, and the cross-sectional area of saidsecond anode flow channel decreases in a flow direction of said fuelalong at least a portion of the length of said second anode flowchannel.
 15. The fuel cell assembly of claim 14 wherein said first anodeflow channel and said second anode flow channel each have asubstantially rectangular cross-section, and a width of said first anodeflow channel decreases in accordance with an exponential function alongsaid at least a portion of the length of said first anode flow channel,and a width of said second anode flow channel decreases in accordancewith an exponential function along said at least a portion of the lengthof said second anode flow channel.